You can download some papers as Postscript or PDF files from the list of my publications below, or you can ask for a hardcopy by mailing me on Maxim.Olshanskii (at) mtu-net.ru

Books and Thesis

Short course on multigrid and domain decomposition methods, Moscow State University: MAKS-Press, Moscow, 2007 (joint with Yu.V.Vassilevski) Full text in russian is available here;

" Lections and exercises in multigrid methods" Fizmatlit: Moscow 2005.

Robust multigrid and preconditioned iterative methods, Habilitation Thesis, (2005) pdf-file (in russian)

Some questions of numerical simulation of unsteady incompressible Navier-Stokes flows in primitive variables, Ph. D. thesis, Moscow State Univ., Dept. of Mechanics and Mathematics, November 1996

Journal papers

• Grad-Div stabilization and subgrid pressure models for the incompressible Navier-Stokes equations, submitted, June 2009, (joint with G.Lube, T. Heister, J.Loewe), pdf-file

• Velocity-Vorticity-Helicity formulation and a solver for the Navier-Stokes equations, submitted, June 3, 2009 (joint with L.G.Rebholz), pdf-file

• Enabling numerical accuracy of the Navier-Stokes-alpha through deconvolution and enhanced stability, submitted, May 2009 (joint with C.C.Manica, M.Neda, L.G.Rebholz), pdf-file

• An iterative method for the Stokes type problem with variable viscosity, submitted, Dec. 2008 (joint with P.Grinevich) pdf-file

• A finite element method for surface PDEs: Matrix properties, submitted, (joint with A.Reusken) pdf-file (updated in June 2009)

• Multigrid analysis for the time dependent Stokes problem, submitted, Sept. 2008, (update in April 2009) pdf-file

• On the accuracy of the rotation form in simulations of the Navier-Stokes equations, Journal of Computational Physics, V. 228 (2009), pp. 3433–3447 (joint with W.Layton, C.C.Manica, M.Neda, L.G.Rebholz), pdf-file

• Error analysis of a projection method for the Navier-Stokes equations with Coriolis force, Journal of Mathematical Fluid Mechanics, DOI 10.1007/s00021-009-0299-0 (joint with A.Sokolov and S.Turek), pdf-file

• Analysis of semi-staggered finite-difference method with application to Bingham flows, Comp.Meth.Appl.Mech.Eng. V. 198 (2009), pp. 975-985 pdf-file

• A Finite Element method for elliptic equations on surfaces, accepted to SIAM J.Num.Anal.(joint with A.Reusken, J.Grande) pdf-file (updated in May 2009)

• Two finite-difference schemes for the Bingham cavity flows, Rus. J. Num. Anal. Math. Model., V.23 (2008), 615--634 (joint with E.Muravleva) pdf-file; preprint in russian is here

• Numerical study of a discrete projection method for rotating incompressible flows, ETNA, V. 32 (2008), 49--62 (joint with A.Sokolov and S.Turek) PDF file and additional resources are downloadable here

• A discrete projection method for incompressible viscous flow with Coriolis force, Comp.Meth.Appl.Mech.Eng. 197 (2008), 4512-4520 (joint with A.Sokolov and S.Turek) pdf-file

• An augmented Lagrangian approach to linearized problems in hydrodynamic stability, SIAM J.Sci.Comp. 30 (2008), 1459-1473 (joint with M.Benzi) pdf-file

• Pressure Schur complement preconditioners for the discrete Oseen problem, SIAM J.Sci.Comp. 29 (2007), 2686-2704 (joint with Yu.Vassilevski) pdf-file

• An augumented lagrangian-based approach to the Oseen problem, SIAM J.Sci.Comp. 28 (2006) 2095-2113(joint with M.Benzi) pdf-file

• Uniform preconditioners for a parameter dependent saddle point problem with application to generalized Stokes interface equations, Numerische Mathematik, 105 (2006),159--191 (joint with J.Peters, A.Reusken) pdf-file

• Analysis of a Stokes interface problem, Numerische Mathematik, 103 (2006),129--149(joint with A.Reusken) pdf-file

• Stabilized finite element schemes with LBB-stable elements for incompressible flows, Journal of Computational and Applied Mathematics, 177 (2005) 243-267 (joint with Gelhard T, Lube G., J.-H.Starcke) pdf-file
  

• Analyis of a multigrid method for convection-diffusion problem with Dirichlet boundary conditions, J.Computational Mathem. and Mathem. Physics. 44 (2004) 1462-1491 pdf-file (in Russian)
  

• Convergence analyis of a multigrid solver for a finite element method applied to convection-dominated model problem, SIAM J.Num.Anal. 42 (2004) 1261-1291 pdf-file (joint with A.Reusken)
  

• Grad-Div stabilization for the Stokes equations, Mathematics of Computation 73 (2004) 1699-1718 (joint with A.Reusken) pdf-file

• A low order Galerkin finite element method for the Navier-Stokes equations of steady incompressible flow: A stabilization issue and iterative methods, Comp.Meth.Appl.Mech.Eng. 191, 5515-5536 (2002) pdf-file
  

• Navier-Stokes equations in rotation form: a robust multigrid solver for the velocity problem, SIAM J.Sci.Comp. 23 (2002) 1682-1706 (joint with A.Reusken) ps-file
  

• Stable finite element calculations of incompressible flows using the rotation form of convection, IMA J.Num.Anal.) 22, 437-461 (2002) (joint with G.Lube ). pdf-file

• On the convergence of a multigrid method for linear reaction-diffusion problems, Computing, 65,193-202 (2000) (joint with A.Reusken) pdf-file

• On the domain geometry dependence of the LBB condition M2AN (Math. Modelling Numer. Anal.) 34 (2000) 935-951 (joint with E.V.Chizhonkov) ziped ps-file

• Iterative solver for Oseen problem and numerical solution of incompressible Navier-Stokes equations, Num. Linear Algebra Appl., V.6, (1999) 353-378 pdf-file

• Effective Preconditioning of Uzawa Type Schemes for Generalized Stokes Problem, Numerische Mathematik V.86, 443-470, (2000) (joint with G.Kobelkov) pdf-file

• Two-Level Method and Some A Priori Estimates in Unsteady Navier-Stokes Calculations, Journal of Computational and Applied Mathematics. , 104,(1999) 173-191 pdf-file

• On the asymptotic of the constant from infsup condition in elongated domains, Mathematical Notes, (Matematicheskie Zametki) V.67, 387-396, (2000) (with Chizhonkov E.V) Russian version of the paper can be downloaded.

• On Simulation of the Outflow Boundary Conditions in FD Calculations for Incompressible Fluid, Int. J. Numer. Meth. Fluids V.33, 499-534, (2000) (with Staroverov V.M.) pdf-file

• On the Stokes problem with model boundary conditions, Sbornik: Mathematics, 188, 603-620, (1997) (English translation from Matematicheskii Sbornik) pdf-file in English ps-file in Russian

• An exact numerical method for solving the Stokes type factorized problem, Journal of Computational Mathematics and Mathematical Physics, 1997, V.37, N2, pp.198-209

• The Stokes problem with a parameter, Journal of Computational Mathematics and Mathematical Physics, 1996, V.36, N2, pp.193-202

• On numerical solution of nonstationary Stokes equations, Russ. J. Numer. Anal. Math. Modelling. 1995, V.10, N1, pp.81-92

• On one iterative method for numerical solution of the Stokes problem, Vestnik MGU, Ser.15, 1993, N2, pp.72-77 (in Russian)

Papers in conference proceedings

• On a robust multigrid method for convection-diffusion finite element problems, (joint with A. Reusken) pdf-file

• A Stokes interface problem: stability, error estimate and a solver, in Proc. of European Congress on Computational Methods in Applied Sciences andEngineering, ECCOMAS 2004 (Eds. P. Neittaanm\"aki, etc.), 2004 pdf-file
  

• Preconditioned iterations for the linearized Navier-Stokes system in the rotation form, Proceedings Second MIT Conference on Computational Fluid and Solid Mechanics, K.J.Bathe, editor, Elsevier (2003) 1074-1077 pdf-file
  

• A robust iterative solver in simulation of unsteady incompressible Navier-Stokes flow, Proc. Fourth Europ. Comput. Fluid Dynamic Conf., V.1, (Eds. R.Papailiou, etc.), Willey, Chichester, etc., 1998, p.1296-1301 ps-file

• On Preconditioning Techniques for Generalized Stokes Problem, Proc. of the Conf. on Precond. Iter. Solution Meth. in Large Scale Probl. in Scientific Comp., eds. O.Axelsson, M.Neytcheva, B.Polman, Nijmegen, the Netherlands, 1997, 137-144

• To numerical solution of the Stokes problem, Proceedings of the conf. on Appl.Math. and Comp.Science, Moscow, 1996, pp.27-39, (with Kobelkov G.M. and Staroverov V.M.)